I suppose you caught the article http://www.cnn.com/2009/US/04/15/octuplet.mom/index.html, or one like it, saying the mother of 8 now seeks to register that name as a trademark, for diapers and TV shows.
She might get a registration. I cannot find any legal reason why not. That would not prevent continued use by news organizations of "OctoMom" as fair use. And she would be a fool to interfere with free publicity.
Monumental bad taste aside, this is a pretty clever move, if she can get her diapers onto the market. Considering the public's bad taste, some manufacturer will surely license her trademark and start selling Octomom diapers.
Only in America.